Connecting processors using twisted torus configurations

ABSTRACT

Methods, systems, and apparatus, including computer programs encoded on computer-storage media, for connecting processors using twisted torus configurations. In some implementations, a cluster of processing nodes is coupled using a reconfigurable interconnect fabric. The system determines a number of processing nodes to allocate as a network within the cluster and a topology for the network. The system selects an interconnection scheme for the network, where the interconnection scheme is selected from a group that includes at least a torus interconnection scheme and a twisted torus interconnection scheme. The system allocates the determined number of processing nodes of the cluster in the determined topology, sets the reconfigurable interconnect fabric to provide the selected interconnection scheme for the processing nodes in the network, and provides access to the network for performing a computing task.

BACKGROUND

The present description generally relates to processor topologies usingtwisted torus configurations

BACKGROUND

Machine learning often requires large amounts of computation andcommunication bandwidth. To provide the needed processing capability,devices such as artificial intelligence (AI) accelerators can be used.In some cases, networks of many interconnected AI accelerators can beused to provide the desired processing capability. More generally,clusters of processors can have different sizes and configurations,resulting in different properties and thus varying levels of suitabilityfor different computational tasks.

SUMMARY

In some implementations, a system provides a large cluster of processingnodes that are connected by a reconfigurable interconnect fabric. Thereconfigurable interconnect network can include switching devices, e.g.,multiplexers or other elements, to selectively enable variouscombinations of direct, physical-layer connections between processingnodes. The processing nodes can be artificial intelligence (AI)accelerator devices or machine learning (ML) accelerator devices, forexample, application-specific integrated circuits (ASICs) such as aTensor Processing Unit (TPU). As a result, the system can provide alarge cluster of accelerators that are configurable in many differentways to achieve the performance characteristics needed for differenttasks.

The system can be implemented as a shared system that allows differentusers to concurrently and remotely access different portions of a largecluster of computing nodes. For example, a host system can dynamicallyallocate groups of processing nodes from a cluster of processing nodesthat may include, for example, hundreds or thousands of differentprocessors. The groups of nodes can be different, distinct propersubsets of the processing nodes in the system. Different users and taskshave different requirements, and so different numbers of processingnodes can be allocated for different situations. For example, differentusers may respectively request different numbers of nodes, typically aspowers of two, e.g., 2, 4, 8, 16, 32, 64, 128, etc. In addition toallowing different numbers of nodes to be allocated, the system canorganize the nodes in different topologies using the reconfigurableinterconnect fabric, e.g., with different arrangements of dataconnections between the nodes. The different networks (e.g., groups ofnodes, potentially with different node interconnection scheme), are thenmade available independently to different users. In effect, a singlelarge physical cluster of processing nodes can be presented to multipledifferent users as virtual clusters configured according to the needs ofthe different users. Each group of nodes forming a virtual clusteroperates separately from the groups of nodes for other users, allowingeach to be isolated from the rest of the network.

One of the benefits of the system is the ability to use differentinterconnection schemes for different node topologies, to improve theperformance of computing tasks performed with different sizes andtopologies of networks. For networks that have a cubical arrangement ofnodes, a torus configuration provides a symmetric network with highperformance. For other network configurations that are not cubical,however, the a twisted torus interconnection scheme can be used. Thiscan provide symmetry to network topologies that would not have beensymmetrical with a standard torus. For non-cubical dimensions of nodes,the twisted torus interconnect can offer higher bisection bandwidth,better load balance characteristics, and lower network diameter. Forexample, interconnecting a group of nodes in a 8×4×4 configuration as a3D twisted torus offers a ˜1.73× increase in effective bandwidth forall-to-all (e.g., uniform random) traffic compared to a traditional 3Dtorus interconnect.

In some implementations, when a user launches a machine learningtraining job through a request to the system, the host loads thetraining data from the storage and set up the environment. This caninclude selecting an appropriate number of nodes, selecting a topologyfor the nodes, and selecting an interconnect scheme for the nodes (e.g.,whether to add a twist to the torus, and if so, to what extent). Thesystem then allocates the network with the selected parameters and makesit available for performing the user's processing task. After thenetwork is established, the ASIC accelerator chips in the networkperform the needed tasks, such as training machine learning models(e.g., neural networks) and communicate with each other through fast,direct connections such as Inter-Core Interconnect (ICI) links. Taskssuch as machine learning model training may require a duration on theorder from seconds up to days, depending on the machine learning modelsize, training data size, and the number of ASIC accelerator chips.During that period, the amount of inter-host communication is much lessthan the ASIC-ASIC communications between processing nodes of anallocated network.

In some implementations, a method performed by one or more computersincludes: providing a cluster of processing nodes coupled using areconfigurable interconnect fabric; determining a number of processingnodes to allocate as a network within the cluster and a topology for thenetwork; selecting an interconnection scheme for the network, whereinthe interconnection scheme is selected from a group that includes atleast a torus interconnection scheme and a twisted torus interconnectionscheme; allocating the determined number of processing nodes of thecluster in the determined topology; setting the reconfigurableinterconnect fabric to provide the selected interconnection scheme forthe processing nodes in the network; and providing access to the networkfor performing a computing task.

In some implementations, selecting the interconnection scheme comprisesselecting between the torus interconnection scheme and the twisted torusinterconnection scheme based on the determined number of processingnodes.

In some implementations, selecting the interconnection scheme comprisesselecting the torus interconnection scheme based on determining that,for a network of a number of dimensions that the reconfigurableinterconnect fabric supports, the number of processing nodes allows thenetwork to have equal size in each of the dimensions. For example, ifthe reconfigurable interconnect fabric enables torus networks of twodimensions or three dimensions, the system can determine if the numberis a perfect square or a perfect cube.

In some implementations, the selected topology has a first size in afirst dimension and a second size in a second dimension. Selecting theinterconnection scheme comprises selecting the twisted torusinterconnection scheme based on determining that the first size is amultiple of the second size.

In some implementations, the selected topology for the network comprisesan arrangement of nodes that extends along multiple dimensions andincludes multiple nodes along each of the multiple dimensions, whereinthe selected topology has different amounts of nodes along at least twoof the multiple dimensions. Selecting the interconnection schemecomprises selecting the twisted torus interconnection scheme such thatthe network is symmetric.

In some implementations, the twisted torus interconnection schemeincludes wraparound connections made using switching elements of thereconfigurable interconnect fabric. Wraparound connections connect nodesor edges of the network that face opposite directions along a samedimension, wherein the wraparound connections for a first dimension inwhich the network is longest do not include any offsets in otherdimensions, and wherein the wraparound connections for a seconddimension in which the network is shorter than the first dimension hasan offset in the first dimension.

In some implementations, the wraparound connections for the seconddimension are each determined by connecting a starting node with anending node that has: (i) a position in the second dimension that is thesame as the starting node, and (ii) a position in the first dimensionthat is equal to a result of a modulo operation involving (a) a sum of aposition of the starting node in the first dimension and a predeterminedtwist increment determined based on the node topology and (b) a lengthof the longest dimension.

In some implementations, selecting the interconnection scheme comprisesselecting the twisted torus interconnection scheme. The method includesselecting an amount of twist and dimensions in which to apply an offsetfor the twist based on lengths of the selected topology.

In some implementations, the selected topology is a two-dimensionaltopology.

In some implementations, the selected topology is a three-dimensionaltopology.

In some implementations, the cluster of processing nodes comprisesmultiple segments having a predetermined size and arrangement ofmultiple processing nodes, the segments having mesh connections betweenthe nodes in each segment. The reconfigurable interconnect fabriccomprises switching elements to permit dynamic, programmablereconfiguration of connections for external-facing data ports ofprocessing nodes in each segment.

In some implementations, the segments are each a 4×4×4 group ofprocessing nodes.

In some implementations, the processing nodes are each separateapplication specific integrated circuits (ASICs).

In some implementations, the reconfigurable interconnect fabriccomprises switches for data-carrying optical signals.

In some implementations, the computing task comprises training a machinelearning model.

In some implementations, the method includes storing multipleconfiguration profiles specifying different configurations of thereconfigurable interconnect fabric to connect subsets of the processingnodes in the cluster; and selecting a configuration profile from amongthe multiple configuration profiles. Switching elements of thereconfigurable interconnect fabric are set according to the selectedconfiguration profile.

In some implementations, the method includes initializing routing tablesfor processing nodes in the network based on stored routing informationcorresponding to the selected configuration profile.

In some implementations, the method includes allocating distinctnetworks of processing nodes for different users from among theprocessing nodes in the cluster, the distinct networks having differentinterconnection schemes.

Other embodiments of this aspect include corresponding computer systems,apparatus, and computer programs recorded on one or more computerstorage devices, each configured to perform the actions of the methods.A system of one or more computers can be configured to performparticular operations or actions by virtue of having software, firmware,hardware, or a combination of them installed on the system that inoperation causes or cause the system to perform the actions. One or morecomputer programs can be configured to perform particular operations oractions by virtue of including instructions that, when executed by dataprocessing apparatus, cause the apparatus to perform the actions.

The details of one or more embodiments of the invention are set forth inthe accompanying drawings and the description below. Other features andadvantages of the invention will become apparent from the description,the drawings, and the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram showing an example of a system for connectingprocessing nodes in different configurations, including twisted torusconfigurations.

FIG. 2A is a diagram showing an example of a torus configuration ofinterconnections for an 8×4×1 topology.

FIG. 2B is a diagram showing an example of a twisted torus configurationof interconnections for an 8×4×1 topology.

FIG. 3A is a diagram showing connections for an example of a torusconfiguration of interconnections for an 8×4×4 topology.

FIG. 3B is a diagram showing connections for an example of a twistedtorus configuration of interconnections for an 8×4×4 topology.

FIG. 4A is a diagram showing connections for an example of a torusconfiguration of interconnections for an 8×8×4 topology.

FIG. 4B is a diagram showing connections for an example of a twistedtorus configuration of interconnections for an 8×8×4 topology.

FIG. 5 is a table showing example twist parameters for sizes ofprocessing node networks.

FIG. 6 is a table showing different node and interconnect configurationsand related characteristics.

FIG. 7 is a table showing different node configurations and uniformrandom bandwidth measures of twisted torus interconnections compared tostandard torus interconnections.

FIG. 8 is a table showing various node network configurations andrelated properties.

FIGS. 9 and 10 are tables showing examples of node networkconfigurations.

Like reference numbers and designations in the various drawings indicatelike elements.

DETAILED DESCRIPTION

FIG. 1 is a diagram showing an example of a system 100 for connectingprocessing nodes in different configurations, including twisted torusconfigurations. The system 100 includes a server system 110 thatprovides access to a cluster of processing nodes 111. The system alsoincludes a client device 104 that a user can use to request processingtasks to be performed using the cluster of processing nodes 111. Theserver 110 and the client device 104 can communicate over a network 140.The client device 104 may be used by one or more users, such as a user102 a, 102 b. Many different client devices can be used to concurrentlycommunicate with the server system 110 and perform computing tasks usingseparate networks that the system 110 allocates from among the nodes inthe cluster 111.

The cluster 111 of processing nodes has a reconfigurable interconnectfabric that enables different configurations of processing nodes. Theserver system 110 includes a management module 112 that can analyze thecomputing needs for a user or task, select appropriate parameters (e.g.,number of nodes, topology of nodes, interconnect scheme, etc.), and thenset switches or other reconfigurable elements of the interconnect fabric(e.g., switching devices 116) to allocate and initialize a node networkwith the selected parameters. The system can support various nodetopologies and interconnect schemes as discussed further below.Typically, the management module 112 allocates small groups of nodeswithin the cluster 111, often using a small fraction of the total set ofprocessing nodes in the cluster 111 and leaving the remaining processingnodes to be allocated in different subsets which may have differenttopologies for different jobs run by different users.

More generally, the management module 112 performs resource allocationto allocate different subsets of the processing nodes in the cluster 111for different tasks (e.g., for the tasks of different users,applications, accounts, sessions, etc.). From a large cluster 111 ofdozens, hundreds, thousands, or tens of thousands of processing nodes,the management module 112 allocates different subsets of processingnodes to operate separately, e.g., independent of the rest of thecluster 111 and with the subsets isolated from each other. For example,the system can dynamically assign an isolated subgraph or sub-network ofprocessing nodes within the overall cluster. This allows the cluster ofprocessing nodes 111 to be shared concurrently for many different usersor tasks, enabling the subsets or subgroups of nodes to run theirrespective tasks independently and isolated from each other. Thearrangement facilitates use as a cloud computing platform, such as forsoftware as a service (Saas), platform as a service (PaaS), machinelearning as a service (MLasS), and other use cases.

In general, the disclosure relates to reconfiguring channels ofcommunication or ports in a high-speed communication network, e.g., anetwork of machine learning accelerators that includes multipleapplication specific integrated circuits (ASICs). Deep learning trainingoften necessitates distributed, parallel processing. The distributioncan either partition the large amounts of training data into differentreplications or replicas (e.g. data parallelism), or partition a verylarge model into smaller modules (e.g., model parallelism). Thepartitioned training data and model parameters are put onto differentprocessing units to compute concurrently.

Distributed training happens in a synchronous, iterative, andincremental loop. Under data parallelism, each processing unit ingests amini-batch of data at each step, computes the local gradients, and thenexchanges all local gradients throughout the network of compute units inan all-reduce manner to compute a final, globally consistent gradient,with which model weights are updated at the end of a step.

Under model parallelism, each processing unit takes model activationinput from its local training data, or from the output of anotherprocessing unit that operates on hidden layers before itself. Theprocessing unit then computes the activation output, which can either bea final model output, or serve as the activation input of anotherprocessing unit. The gradient is computed on the processing unit thatincludes the final layer, and gets sent back to the previous layers toupdate the partitioned submodels. This process can be pipelined tooperate on successive mini-batches. Under this approach, intermediateactivation output is sent around the network, as well as the gradientsat the model partitioning boundaries.

In practice, data and model parallelism can be combined to achieve thehighest performance. For example models with hundreds of billions ofweight parameters, a huge amount of compute resources and communicationsare needed to converge the model to the level of accuracy required.

To speed up the training process, ASICs such as the custom-builtaccelerator chip the Tensor Processing Unit (TPU) are designed to serveas processing nodes in order to speed up deep learning computationtasks. In some implementations, other accelerator chip types are used asprocessing nodes (e.g., FPGAs, GPGPUs, or CPUs). Meanwhile, aco-designed inter-accelerator high-speed communication network is alsobuilt to speed up the inter-processing unit communication. Altogether,the training system can provide exaFLOP-level compute performance,equivalent to a state-of-the-art supercomputer.

The TPU accelerator's custom-built network is designed for simplicity inorder to reduce the network processing overhead. With the fundamentalfeatures of an interconnected network complete, such as addressing,error detection and correction, routing and flow control, the bulk ofnetwork processing is carried over on the accelerator chip hardware tospeed up processing.

The solutions disclosed herein apply to the synchronous data-paralleland model-parallel training pattern discussed above, and also apply toasynchronous, distributed training in an accelerator network in general.

The components of the system 100 can be interconnected by any form ormedium of digital data communication (e.g., a communication network 140such as the Internet).

The cluster of nodes 111 can include many different processing chips(e.g., ASICs) that provide the processing nodes. The system 110 can be ashared system that allows multiple users to use the system concurrently.The system 110 can allocate subsets of the processor and allocate groupsof the processing nodes for different users.

The different processing nodes can be interconnected by wires and/oroptical links to be able to transfer data between them. Theinterconnections can be coupled through switches that allow dynamicchanges to the interconnections between processing nodes. For example,the system 110 can allocate a group of processing nodes for a user andset the switches to isolate that group from the rest of the cluster 111.The system can present a smaller group of nodes to the user, e.g., asubset of 64 or 128 interconnected processing nodes out of thousands inthe overall cluster 111 processing data separately from the rest of thecluster.

The nodes in the cluster 111 can be conceptually organized intodifferent dimensions with nodes being indexed with coordinates, e.g., X,Y, and Z coordinates. A subset can be allocated with a cubical topology,e.g., with a size of 4 for each of the three dimensions (e.g., 4×4×4)for a cube topology having a total of 64 nodes. Cubical configurationscan interconnected in a 3D torus configuration, in which every node isconnected to its neighboring nodes one unit distance away. Each nodewould be connected to six other nodes, one node in each direction alongeach of the X, Y, and Z directions (e.g., +/−1 unit in each of X, Y, andZ). At the edges or surfaces of the cube shape, where the nodes do nothave an immediate neighbor in a certain direction, the 3D torus providesa connection that wraps around to the opposite side. For example, for a4×4×4 cube arrangement, the node at coordinate (0, 0, 0) would have aconnection that wraps around to connect with the node at (3, 0, 0).These wraparound connections provide symmetry for the paths and providehigh efficiency.

The system can provide groups of processing nodes in cubical topologies(e.g., 4×4×4, 8×8×8) that use a 3D-torus interconnections amongprocessing nodes.

The system can also provide groups of processing nodes in non-cubicalconfigurations (e.g. 8×4×4, 8×8×4) interconnected as twisted toritopologies. For non-cubical dimensions of nodes, the twisted torusinterconnect can offer higher bisection bandwidth, better load balancecharacteristics, and lower network diameter. For example,interconnecting a group of nodes in a 8×4×4 configuration as a 3Dtwisted torus offers a ˜1.73× increase in effective bandwidth forall-to-all (e.g., uniform random) traffic compared to a traditional 3Dtorus interconnect. This technique can be implemented with a clusterthat has only partial reconfigurability in the interconnect fabric, suchas reconfigurability at only certain edges or interfaces.

In some implementations, the cluster of processing nodes 111 is formedof small units or “segments” that each include multiple processing nodesand connections among the nodes in the segment. The use of separatesegments can facilitate partitioning and failure isolation. Typically,the segments each generally have the dimensions and topology. As anexample, the segments can each be arranged in a 4×4×4 topology, e.g.,with 64 nodes in a cubical arrangement. Other segment types may be used,such as 2×2×2, 2×2×1, 4×4×2, and so on. Within an individual segment,the nodes may be permanently or non-reconfiguably connected, e.g., in amanner that the interface ports are not reassignable outside the segmentor at all.

Nodes within the segment are 3D-mesh connected. In other words, if theprocessing nodes are considered to occur along three axes, X, Y, and Z,each node can connect with its six neighbors (e.g., the nodes atpositions before and after in each of the three dimensions). At thesides of the segment, such as the faces of the cube formed by a 4×4×4segment topology, there are data ports that are available to connect tothe exteriors of other segments. The connections at these external facesof the segment topology can be routed to switches, such as opticalcircuit switches. The switches can be configured to selectively connectthe segments together into larger topologies. For example, the switchescan be used to connect adjacent sides and extend the 3D mesh between toany appropriate combination of segments working together. For example,the system can connect two 4×4×4 segments into a 8×4×4 topology, connectfour 4×4×4 into an 8×8×4 topology, and so on. In general, groups ofsegments can be connected to achieve any topology of “4s×4t×4u” 3D torusfor integer values of s, t, and u.

The processing nodes may be allocated in and used in different nodalconfigurations (e.g., topologies) as sub-networks within the cluster111. Different configurations may include different numbers ofprocessing nodes and different arrangements of the nodes. In general,node configurations often include arrangements of nodes in two or threedimensions, with mesh connections between the adjacent nodes. The meshconnections refer to bidirectional connections between each node withits neighbors along the grid dimensions, X, Y, Z. A two-dimensionalconfiguration may have nodes at integer positions along an X-Y grid,e.g., a 4×4 configuration representing 16 nodes arranged in a square, a8×4 configuration representing 32 nodes in a rectangle with 8 nodesalong the X dimension and 4 nodes along the Y dimension, and so on.Three dimensional configurations have positions assigned in threedimensions, X, Y, and Z, e.g., a 4×4×4 configuration having 64 nodes anda length of four along each dimension, a 8×4×4 configuration having 128nodes with a length of 8 along the X dimension and lengths of four nodesalong the Y and Z dimensions, and so on.

Different configurations (e.g., sizes and arrangements of sub-networksof processing nodes) can be selected by the server 110 to meet the needsof different users and tasks. The system 110 can also choose and applydifferent interconnect arrangements for different node networks, forexample, torus interconnect arrangements or twisted torus interconnectarrangements.

The management module 112 may select a particular network configurationfor the nodes in the cluster 111 and reconfigure the connections among aportion of the cluster 111 to provide the selected networkconfiguration. The server 110 may select the number of nodes in asub-network and the particular network configuration for the nodes basedon one or more factors, such as the specific task or job that the nodeswill be used to perform, the type of task or job that the nodes will beused to perform, the user requesting a task or job, a group of usersthat a user requesting a task or job belongs to, an application thatwill be used to perform a task or job with the nodes, or a type ofapplication that will be used to perform a task or job with the nodes.Although examples discussed below may describe selecting a networkconfiguration based on a particular task/job or a particular type oftask/job, other factors may be used in addition to or in place oftask/job factor(s) for selecting a particular network configuration fora group of nodes.

Each of the nodes may have multiple data ports (e.g., ICI ports). Thenodes may be part of chipset, such as an artificial intelligenceaccelerator application-specific integrated circuit (ASIC). One exampleof an ASIC would be a tensor processing unit (TPU). Each node mayrepresent a chip on one or more chipsets. For example, each chipset mayinclude four chips that each serve as a node. Each chipset may furtherinclude one or more switching devices for each of the nodes, such as oneor more multiplexers (e.g., ICI multiplexers) that are used toreconfigure the network configuration.

The client device 104 may be, for example, a mobile computing devicesuch as a smart phone, a mobile phone, a table computer, a smart watch,a laptop computer, a PDA, etc. The client device 104 may be a desktopcomputer, a server, or part of a server. The client device 104 mayinclude a storage device. The client device 104 may include memory, suchas RAM (e.g., DRAM, SRAM, etc.).

The network 140 may be a local area network (“LAN”), a wide area network(“WAN”), a peer-to-peer network (having ad-hoc or static members), agrid computing infrastructure, or the Internet.

As illustrated in FIG. 1, users 102 a, 102 b each separately send arequest 106 a, 106 b to the server 110 over the network 140. Therequests 106 a, 106 b may correspond to or specify a task or type oftask to be performed by the cluster 111 of processing nodes. Forexample, the task may training of a machine learning model, such as aneural network. For example, the requests 106 a, 106 b may be sent, inresponse to input from the respective users 102 a, 102 b, to initiateprocessing of two different machine learning tasks. The requests 106 a,106 b may include additional information, such as an indication of theclient device 104 a, 104 b, user 102 a, 102 b, account or organization,or other information related to the request 106 a, 106 b.

The server 110 provides each request 106 a, 106 b to the managementmodule 112, which selects a number of nodes to use for each request, aconfiguration of the nodes, and an interconnection scheme for the nodes.The management module 112 then allocates and initializes a network foreach user and then provides each user 102 a, 102 b access to his or herrespective network within the cluster 111. An example of the process ofselecting a number of nodes and other configuration parameters is shownfor the two different users.

The management module 112 can determine a number of nodes to be used foreach user (150). For example, users may specify a number of nodes touse, and that can be transmitted in a request 106 a, 106 b. As anotherexample, the nature of the task, size of a data set to be used, timeconstraints or targets for completion of the task, cost or resourcelimits, and other parameters may be used to select an appropriate numberof nodes to be used. In the example, the system determines that 64processing nodes should be used for user 1's task and 128 processingnodes should be used for user 2's task.

The management module 112 determines if the number of nodes allows for atopology with equal values for each of multiple dimensions (160). Forexample, a number of nodes that can be expressed as n{circumflex over( )}2 for an integer n allows a square topology in 2 dimensions (e.g.,the number of nodes is a perfect square such as 4=2{circumflex over( )}2, 9=3{circumflex over ( )}2, 16=4{circumflex over ( )}2, etc.), anumber of nodes that can be expressed as n{circumflex over ( )}3 for aninteger n allows a cubical topology in 3 dimensions (e.g., a number ofnodes is a perfect cube such as 8=2{circumflex over ( )}3,27=3{circumflex over ( )}3, 64=4{circumflex over ( )}3, etc.), a numberof nodes that can be expressed as n{circumflex over ( )}4 for an integern allows a topology with an equal size in each of 4 dimensions (e.g., anumber of nodes such as 16=2{circumflex over ( )}4, 81=3{circumflex over( )}4, 256=4{circumflex over ( )}4, etc.), etc.

The system can check for each number of dimensions that the cluster hasconnectivity to support. For example, one network may have sufficientswitching capability, data ports, and connections to allowone-dimensional torus arrangements (e.g., a single node or line of nodes2×1, 3×1, etc.), 2D torus arrangements, and 3D torus arrangements.Another cluster with a different reconfigurable fabric may provide moreswitches, connections, and data ports for nodes to additionally support4D torus interconnections and/or 5D torus interconnections.

This determination is one of the factors that can affect which nodetopology and interconnect scheme is used. In the case of user 1, thenumber of nodes selected, e.g., 64, is a perfect cube, e.g.,4{circumflex over ( )}3. For user 2, the number of nodes selected, e.g.,128, is not a perfect cube and so does not support a cubical topology.In the example, the cluster 111 and associated interconnect fabricsupports networks of 1, 2, and 3 dimensions. Although a network 128nodes could be provided by a 7-dimensional network of size 2, thecluster 111 and reconfigurable interconnect in this example do notsupport 7-dimensional networks.

The management module 112 selects a node topology and interconnectscheme for each network to be used (170). When the set of availablenodes is a perfect cube, the system can arrange the nodes in a cubicalconfiguration, e.g., 4×4×4, 8×8×8, 12×12×12. The nodes within the cubeare connected in a mesh interconnection, with bidirectional data linksbetween each adjacent node. For the connections at the outer faces ofthe cube, wraparound connections can be made to form a torusconfiguration. That is what the management module 112 selects for thenetwork for user 1.

For networks of nodes that do not have an amount of nodes that is aperfect cube, a cubical topology of nodes is not possible. Othernon-cubical topologies may provide better performance using a twistedtorus interconnection than a standard torus interconnection. Asdiscussed below, the system can use twisted torus configurations toprovide symmetrical networks for non-cubical node topologies. For user2, the management module 112 selects an 8×4×4 topology of nodes and atwisted torus, where wraparound connections in the Y and Z dimensionsinclude offsets in the X dimension, as discussed further below withrespect to FIGS. 2A-8. Twisted torus interconnections can provide morebalanced, more symmetrical networks and higher performance than standardtorus interconnections for non-cubical node topologies.

The server system 110 can store various configuration profiles 180 thatindicate different node topologies and interconnect schemes, as well asswitch settings (e.g., settings for switching elements) to achieve thedifferent configurations. The selection of node topologies andinterconnects can include selecting for each user a configurationprofile from among profiles for multiple possible configuration, e.g.,where the configurations may have different numbers of nodes, differentnode topologies, and different interconnect schemes. In some cases, themanagement module 112 may adjust the number of nodes to be used orconsider other factors in selecting the topology and interconnectscheme. For example, the constraints for a user may specify a range ofamounts of nodes (e.g., between 40 and 80 nodes, or at least 50 nodes,etc.), and the management module 112 can select a particular number ofnodes that allows for a favorable topology. For example, if at least 50nodes are requested by a user, the system may increase to 64 to be ableto provide a cubical topology. In general, the system may supportnetworks of certain discrete amounts of nodes and then select the nextclosest number that corresponds to one of the available configurationsdescribed by one of the configuration profiles 180.

In cases where the user does not specify a number of nodes (e.g., aspecific number or at least a minimum desired number of processing nodesto use), the system may obtain information about a processing task anduse that information to determine a number of nodes that should be used.In some cases, this may be done by profiling or classifying the task ordata set to be used and determining constraints for the task. Forexample, the computer system 110 can estimate aspects of the processingtask such as a type or category of the task (e.g., training a neuralnetwork, video rendering, etc.), an application or function to be used,a number of threads, software functions to be performed and expected ortypical amounts and types of operations performed by those functions(e.g., amounts and integer, floating point, vector multiplication, analgorithm to be used (e.g., a particular machine learning model trainingalgorithm), parameters for the algorithm (e.g., a learning rate, etc.),characteristics of a machine learning model to be trained (e.g., size orstructure of the model, such as a number of trainable parameters in aneural network model, a number of neural network layers in the model,types of neural network layers in the model, etc.), an amount or type oftraining data to be used (e.g., number of examples, storage size of thedata, etc.), a number of training iterations or epochs expected, and soon. The system 110 can also determine constraints for the task, such asa time needed for completion (e.g., a target completion time ordeadline), an accuracy of output desired for the model after training, aminimum or maximum level of resources to be allocated to the task, andso on. From the data characterizing the nature of the task and theconstraints for the task, the system can determine a level of resourcesand type of resources appropriate for the task, e.g., that are expectedto complete the task and meet the constraints. This can be expressed ina number of ways, such as an amount of operations or rate ofmathematical operations, a bandwidth or latency level needed, aclassification of the complexity or computational demands of the task(e.g., class 1, class 2, or class 3, representing different levels ofprocessing complexity), and so on. The number of nodes to allocate forthe task, and/or a preferred interconnect topology, can be determineddirectly for the task or based on the other measures of resources neededfor the task.

Whether the level of processing resources needed is specified by a useror determined by the system, the server system 110 can store and use atable or other data that maps processing requirements (e.g., whetherexpressed in individual node amounts, a class or range for a nodeamount, or another measure of processing capability) to correspondingtopologies. For example, the table can indicate the differentconfigurations provided by the configuration profiles 180 and map themto different numbers of nodes. Once a number of processing nodes isdetermined, or at least a class or range of processing capability isdetermined for a task, the system 110 can look up in the table whichconfiguration profile 180, e.g., which topology and interconnectionscheme, best suits the task.

FIG. 9 shows an example table 900 that maps numbers of nodes todifferent network topologies. The example limits network dimensions tomultiples of four and allows 2D and 3D topologies. Each of thetopologies provides a symmetric network. For example if a task isdetermined to need approximately 8 nodes, the first entry in the tabledirects the system 110 to use a 4×4 topology with a 2D torusinterconnection. The networks that use standard torus configurations areindicated in bold. The configurations with twisted torus connectionsprovide additional options for symmetric networks for numbers of nodesthat are in between the numbers that permit square or cubical networkswhere a standard torus is symmetric. For example, for a network size of32 nodes, a symmetric network can be provided with an 8×4 twisted torusconfiguration, providing significantly better performance than an 8×4standard torus and providing an option for a symmetric network muchsmaller than the 64 nodes of an 8×8 topology or a 4×4×4 topology.

FIG. 10 shows an example table 1000 that gives various examples ofsymmetric networks with different topologies and node configurations.This example does not constrain the network size to have dimensions thatare multiples of four. The entries in FIG. 10 represent differentoptions for networks that the system 110, and but the system 110 is notrequired to directly select the specific configuration listed for aspecific number of nodes. For example, there are two different entriesthat can provide a symmetric network with 8 nodes. The system 110 couldfurther select between these options based on the different performancecharacteristics and network properties (e.g., network diameter, averagehops from one node to another, etc.). Similarly, if 25 nodes areindicated to be used for a task, the system 110 may determine thatmoving up to 27 nodes to allow the 3×3×3 3D torus configuration wouldprovide significant performance benefits over the 5×5 2D torusconfiguration.

FIG. 10, like FIG. 9 and the other tables herein, is not intended to becomprehensive. Rather, it shows that the ability of the system 110 toselectively configure networks of different sizes and in torus ortwisted torus interconnect schemes provide significant versatility tothe system 110. In particular, the system 110 has the ability to choosefrom among many different topologies and interconnection types toprovide symmetric networks for many different sizes (e.g., manydifferent numbers of nodes). This allows performance to scale moreevenly for networks of different sizes, using twisted torusinterconnections to decrease the performance penalty of using networksof sizes between perfect squares for 2D networks and between perfectcubes for 3D networks.

In some cases, there are multiple symmetric network configurations thatcan be used for the same number of nodes. Typically, topologies withhigher dimensions (e.g., 3D vs 2D) and more similar sizes for thedimensions (e.g., 4×4 rather than 8×2) are preferred due to betterlatency and bandwidth performance. Although not illustrated in FIGS. 9and 10, entries in tables of configuration types and the configurationprofiles 180 themselves can include or be labeled with performancecharacteristics, so the system can select the configuration that is mostappropriate for the performance needs of the task. For example, forexample, the system 110 can select the smallest network (e.g., networkwith the fewest nodes) that meets a minimum performance level, or selecta configuration that has the highest performance level given aconstraint on a maximum number of nodes.

As another example, the server system 110 can have rules that assesswhether different conditions a processing task are met, with differentcombinations of conditions being met leading to different topologyselections. For example, the system 110 can use a decision tree to useproperties of a task and/or properties

Although the disclosure emphasizes the use of symmetric networks, theserver system 110 also has the option of using standard torusinterconnection schemes, even for non-perfect-square andnon-perfect-cube numbers of nodes, and the server system 110 may includeconfiguration profiles 180 for these configurations and use them ifdesired to obtain a network with a number of nodes matching a certainnumber or in a certain range.

After a configuration is selected for each user, the management module112 allocates a set of nodes to have the selected topology. Themanagement module 112 also sets values of the interconnects for thenetwork to have the desired interconnect scheme. These settings can bespecified in an appropriate stored configuration profile 180 for thedesired configuration. The node networks can each use routing tables topass information among the nodes in the network. As part of initializinga network, the management module can access stored data, e.g., routingtables 182, that specifies the routing parameters for each node in anetwork, to populate the routing table for each node of each networkallocated. Each configuration profile 180 can have a corresponding setof routing tables 182 that are used for the respective nodes of theconfiguration.

The configuration profiles 180 may indicate switching instructions 114to accomplish the outlined port interconnections. These switchinginstructions may be in the form of multiplexer control inputs (e.g.,that each receive a bit of 1 or 0) or may be expressed in other forms.The switching instructions 114 may include a set of instructions foreach node in the group of nodes allocated, if all nodes havereconfigurable connections for their data ports. In otherimplementations, segments of a certain size (e.g., slices of 4×4 nodesor cube-shaped blocks of 4×4×4 nodes) may use a fixed (e.g.,hardware-defined, non-switchable) interconnect within the segment, andreconfiguration is supported only at the edges or outer faces of thesegment. In these implementations, the switching instructions 114 mayinclude settings for only the outer data ports that are madereconfigurable with switching devices 116.

The management module 112 may provide the switching instructions 114 toswitching devices 116. The switching devices 116 may include, forexample, at least one switching device corresponding to each of thenodes that has a data port configured to permit reconfigurability. Forexample, if standard segments of 4×4×4 nodes are used, then eachstandard-sized segment has 64 nodes, and there are 6 faces to the cube,with each face having 16 nodes and thus 16 available data ports forinterconnections. Although each of the nodes has at least six dataports, the nodes near the center of the cube have all six data portsconnected with neighboring nodes in the predetermined (and potentiallyfixed) mesh connections. Nodes at the outer faces of the cube have oneor more available data ports (e.g., where the nodes do not have aneighbor along one of the X, Y, or Z dimensions) that can be used toform interconnections with nodes at other faces of the same segment orwith nodes at the outer face of a different segment. The switchingdevices 116 may be optical switches, e.g., switches for data-carryingoptical signals.

As a result, the management module 112 allocates and initializes thenetwork for each user, e.g., by allocating or reserving specific nodesin the cluster 111, setting the switching devices 116 to provide thedesired interconnect scheme, setting the routing tables 182 appropriatefor the selected configuration profile 180. The server system 110 thenprovides the users to the networks allocated for them. In other words,the system 110 concurrently provides the two users access to separate,distinct networks within the cluster 111, where the two networks canhave different numbers of nodes, node topologies, and interconnectschemes to best meet the needs of the user's workload.

After the node networks for the users are allocated and initialized, themanagement module 112 may determine application instructions 118 to runan application 120. The application instructions 118 may be extractedfrom the request 106 a, 106 b or generated from a request. Theapplication 120 then carry out the task corresponding to the request 106a, 106 b. As a result of running the application 120, results 122 a, 122b are generated. The results 122 a, 122 b may be sent by the server 110to the respective client devices 104 a, 104 b over the network 140.

FIG. 2A is a diagram showing an example of a torus configuration ofinterconnections for an 8×4×1 topology. FIG. 2A shows a node network 200having an 8×4 configuration of nodes and a torus interconnectarrangement. The network 200 is built from two 4×4 sub-meshes 210 a, 210b that have a mesh interconnection within each sub-mesh and also at theboundary of the two sub-meshes 210 a, 210 b. Wraparound connections,wrapping around in the Y dimension (shown vertically) and in the Xdimension (shown horizontally) complete the torus topology.

The network 200 represents a small subset of the much larger cluster 111of processing nodes. Connections between at least some of the nodes canbe changed using the switches in the reconfigurable interconnect fabric.In some implementations, one or more connections to each node may bereconfigurable by switches. In other implementations, only a subset ofconnections are reconfigurable and/or only a subset of the nodes haveany reconfigurable connections. For example, network segments of 4×4nodes, e.g., the two submeshes 210 a, 210 b, may be multi-node unitswithin the cluster 111 that have fixed mesh connections within thesegment but reconfigurable connections at the edges. Whicheverimplementation is used, reconfigurable switching hardware is used to setthe connections (i) between the two submeshes 210 a, 210 b in the Xdimension where the submeshes are adjacent, (ii) for the X-dimensionwraparound connections, which also connect the submeshes, and (iii) forthe wraparound connections in the Y dimension, which connect eachsubmesh back to itself in this torus arrangement. The connections thatcarry data between nodes can be electrical connections, opticalconnections, or connections through another data carrying medium. Insome implementations, the reconfigurable connections are switchedoptical data connections, and the mesh connections within a submesh mayor may not be optical connections.

The diameter of the network 200 is 6 hops. In the torus configuration,the links that wrap around in the Y dimension do not vary in positionalong the X dimension. For example, the wraparound connection 220extends from the node 221 at position (0, 3) to the node 222 at position(0, 0).

FIG. 2B is a diagram showing an example of a twisted torus configurationof interconnections for an 8×4×1 topology. FIG. 2B shows a node network250 having the same 8×4 configuration of nodes as before, but with atwisted torus interconnect arrangement for those nodes. The network 250includes two 4×4 sub-meshes 260 a, 260 b having a mesh interconnectwithin each sub-mesh and also at the boundary of the two sub-meshes 260a, 260 b. As with the node network 200, the node network 250 is anexample of one of the many different networks that can be allocated inthe cluster 111 and used in parallel with other networks that areseparately allocated to other users.

The difference from the previous diagram is a rewiring of theY-dimension wraparound connections using the switches of thereconfigurable interconnect fabric. In the network 250, connections thatwrap around in the Y dimension also provide an offset in the Xdimension, specifically an X-direction increment by 4. As a result, aconnection 270 from node 271 at position (0, 3) wraps around in the Ydimension and shifts+4 in the X direction to reach node 272 at position(4, 0). This Y-dimension twist is stated as “Y: X+4”, meaning that forY-dimension wraparound links, the system also increments the Xcoordinate by 4.

To account for an X-direction wraparound that may occur by incrementingby four, the system uses a modulo operation, to determine the remainderthat results from dividing by the length of the network 250 in the Xdirection, which is 8 in this example. For example, from node 271, thesystem (i) starts with the X value of 0, (ii) increments by 4, then(iii) computes 4 mod 8=4, with the modulo result (e.g., remainder ofdividing by 8 in this case) as the X value for the other end of theconnection 270. For another node 273 at position (5, 3), the systemwould increment the value of X by 4, compute 9 mod 8=1, and then use themodulo result as the X value for the node at the other end of theconnection, e.g., node 274 at position (1, 0).

When all of the Y-direction wraparound links are made in this manner,the resulting 8×4 twisted torus is completely symmetric. Also, thediameter of the network 250 is 4 hops, which is a reduction compared tothe non-twisted torus configuration.

The system determines whether the twisted torus configuration should beused, the amount of twist, and the dimension(s) in which to add thetwist based on the number of nodes and the arrangement. For example, thesystem adds a twist when the node arrangement has different sizes fordifferent dimensions. A square arrangement (e.g., 4×4, 8×8, etc.) orcube arrangement (e.g., 4×4×4, 8×8×8, etc.) is balanced and does notneed any twist to achieve symmetry. On the other hand, when thearrangement is longer in one dimension than another (e.g., 8×4, 16×8,8×4×4, 8×8×4, etc.) the standard torus wraparound in the longestdirection connects a series of nodes that is greater than thewraparounds in the shorter direction(s).

For example, in FIG. 2A, the X-direction wraparound links wrap around aspan of 8 nodes, so it would be 8 hops to travel around an entire row inthe X direction and arrive at the starting node. On the other hand, theY-direction wraparound links wrap around a span of 4 nodes, and so itwould be only four hops to travel around in the Y direction. This showsthe asymmetry for data transfer when a network with different sizedsides is used. The twist is used to compensate for the asymmetry. Forexample, in FIG. 2B, the offset of four in the X direction (which ishalf the length of the network 250 in the longest dimension, the Xdimension) increases the length of a cycle that moves along the Ydirection. Starting at the node (0,0) and moving up in the Y directionleads to node 271 at position (0, 3), and the connection 270 leads tonode 272 at position (4, 0); continuing to increase in the Y directionanother four steps reaches node (0, 0) through another twistedwraparound link. Thus, the twist increased the length of a cycle forY-direction to 8 hops, the same as the length of an X-direction cycle,to provide full symmetry to the network 250.

In general, the system adds twists to the wraparound links in each ofthe dimensions that are less than the dimension with the largest size.This effectively increases the cycle length for the shortest dimensionsto be closer to or equal to the cycle length for the largest dimension.This technique can be used for many different node arrangements, but itworks especially well when the largest dimension is a multiple of thesmaller dimensions. For example, in FIG. 2B, the node topology is 8×4,and the size in the X dimension is twice the size of the Y dimension. Asa result, routing the Y-dimension wraparound links to create Y-dimensioncycles that each pass through two columns creates the desired level ofsymmetry. As another example, for a topology of 12×4, the size in the Xdimension is three times the size in the Y dimension. The twist in thewraparound for the Y dimension can have an X dimension offset of 4units, so that three columns of four nodes are connected together, sothat moving in the Y direction provides a cycle of 12 hops, equivalentto the length of the X-dimension cycles.

The examples of FIGS. 2A and 2B show two-dimensional node topologies(e.g., there is only one node in the Z dimension), the same techniquescan be used for topologies of 3, 4, 5 or more dimensions. For example,for a three-dimensional node topology, a twist or offset can be providedfor the wraparound connections for any or all dimensions which have asize less than the largest size of the dimensions. For example, if athree-dimensional topology is largest in the X dimension and smaller inthe Y and Z dimensions, then a twist can be included for the wraparoundconnections of both the Y and the Z dimensions.

Following the notation discussed above, some examples of torus andtwisted-torus connectivity are provided below. The examples emphasizethe settings for the reconfigurable switches, which can be providedusing optical switching, electrical switching, or other techniques. Theexamples involve networks composed of units that are multiples of four,e.g., 4×4 sheets or 4×4×4 cubes. This allows the range ofreconfigurability that the interconnect system needs to support to belimited, e.g., to be able to provide offsets and shifts that aremultiples of four rather than every possible increment. This reduces theamount of switching hardware needed and can increase physical density ofthe system. As a result, in the three-dimensional examples in FIGS.3A-3B, 4A-4B, a specific 4×4×4 segment is referred to using thelexicographically smallest node coordinates within that segment. Inthese examples, there are two segment faces for each dimension of thenetwork, referred to as D[in] and D[out], where D is the dimension: X,Y, or Z. In other words, at the exterior of the 3D topology (e.g., arectangular prism shape) there are six total faces: one oriented facingtoward the increasing X direction, one facing toward the decreasing Xdirection, one oriented facing toward the increasing Y direction, onefacing toward the decreasing Y direction, one oriented facing toward theincreasing Z direction, and one facing toward the decreasing Zdirection.

When limiting the size of the topology to be a multiple of four, andthus using 4×4×4 units to compose each network topology, the face orside of each 4×4×4 unit exposes 16 processing nodes, each of which hasan available data port (e.g., a bidirectional data port) that can beassigned outside the unit. As a result, each face of a 4×4×4 segment has16 data ports. When two segments are adjacent to each other, aface-to-face connection is created using the reconfigurable switches,each of the 16 individual data ports on one face are connected to theports in the same relative position on the adjacent face of theneighboring unit. Only faces in the same orientation are connected. Forexample, for two network segments aligned along the X dimension, theface of the first segment that faces toward the increasing X directionwould have each of its nodes connected to the adjacent nodes of the faceof the second segment that faces toward the decreasing X direction,forming a 8×4×4 network.

FIG. 3A is a diagram 300 showing connections for an example of a torusconfiguration of interconnections for an 8×4×4 topology of nodes. Thisconfiguration is composed of two 4×4×4 network units, labeled A and B,that are aligned along the X dimension. In this arrangement, thetopology is longest in the X dimension (e.g., 8 nodes), and shorter inthe Y and Z dimensions (e.g., 4 nodes each).

A table 300 illustrates an example of a wraparound connection in thetorus. For simplicity, only the connections for each face of the 4×4×4segments are shown. Each row in the table 300 represents the connectionbetween a pair of faces. Each row represents 16 node connections,because there are 16 nodes at each face being connected. The [in] facesegments and [out] face segments refer to the coordinate for the lowerleft node of each segment. For example, (0,0,0) refers to segment A, and(4,0,0) refers to segment B.

The 3D torus interconnect provides wraparound connections for eachdimension with no offsets or increments in other dimensions, so thecycle lengths when moving in the X, Y, and Z directions are 8, 4, and 4respectively. For example, the first row in the table 300 shows that theleft face of segment A (e.g., “A_(−X)” or the face of segment A thatfaces the decreasing X direction) connects to the right face of segmentB (e.g., “B_(+X)” or the face of segment B that faces the increasing Xdirection). The second row shows that the left face of segment Bconnects to the right face of segment A, and so on. For the wraparoundconnections in the Y and Z dimensions, each segment's faces in thatdirection connect to each other, e.g., A_(−Y) connects with A_(+Y),A_(−Z) connects with A_(+Z), B_(−Y) connects with B_(+Y), and B_(−Z)connects with B_(+Z).

FIG. 3B is a diagram 350 showing connections for an example of a twistedtorus configuration of interconnections for an 8×4×4 topology of nodes.Compared to the interconnections of FIG. 3A, the X dimension connectionsare unchanged, but the connections for the Y and Z dimensions havetwists added. Following the wraparound connections for the Y and Zdimensions now passes through both segments A and B rather than a singlesegment. The cycle lengths when moving in the X, Y, and Z directionseach have a length of 8. For the wraparound connections in the Y and Zdimensions, each segment's faces in that direction connect not to thesame segment but the other segment, e.g., A_(−Y) connects with B_(+Y),A_(−Z) connects with B_(+Z), B_(−Y) connects with A_(+Y), and B_(−Z)connects with A_(+Z).

FIG. 4A is a table 400 showing connections for an example of a torusconfiguration of interconnections for an 8×8×4 topology. Thisconfiguration has four 4×4×4 network segments, labeled A, B, C, and D,that are aligned with two adjacent to each other along the X dimensionand two more aligned above in the Y dimension. The configuration isdescribed using the same notation discussed above for FIGS. 3A-3B, witheach connection between faces representing 16 individual bidirectionalconnections between the nodes of the faces being made by thereconfigurable switching interconnect fabric.

FIG. 4B is a table 450 showing connections for an example of a twistedtorus configuration of interconnections for an 8×8×4 topology. In the8×8×4 configuration the longest size in any dimension is 8 nodes, andboth the X and Y dimensions have this size. As a result there is notwist needed for the wraparound links in the X and Y dimensions.However, the Z dimension is shorter, and so a twist is added in both theX and Y dimensions for the Z wraparound links. As a result, the Zwraparound connections are incremented by four in both the X and Ydimensions. All of the Z wraparound links then form cycles of 8 nodes byspanning two different segments.

The same techniques can be used for other configurations. For example,in a 12×4×4 configuration there would be three 4×4×4 segments, and twistcould be added for the Y and Z directions so that each cycle passesthrough all three segments in order to increase the cycle length to beequal to the X-dimension cycle length of 12. Passing the connectionsthrough the Various examples use network segment blocks of 4×4×4, butother sizes can be used, e.g., 2×2×2, 3×3×3, 8×8×8, etc. In addition, insome cases a network may support full configurability so that networksare built of individual nodes rather than multi-node segments or blocks.

FIG. 5 is a table 500 showing example twist parameters for sizes ofprocessing node networks. The system 100 discussed above can use thetwisted torus configuration for various node topologies to provide moreefficient networks of processing nodes. In some implementations, theswitching networks among the processing nodes are not arbitrarilyflexible (e.g., do not support every possible twist or configuration),but do support twists where the increment along dimensions meets somecriterion, such as being multiple of two, being a four, or otherparameter that the system is designed to support.

The switches that provide the ability to provide or change the twist forwraparound links allow the system to handle some important cases,illustrated in the table, and include twists to make the networkssymmetric. The first case is the two-dimensional network in which ondimension is twice the other, e.g., 2k×k. In this case, the twist is thelength k of the smaller length (e.g., half the larger length). Thesecond case is a three-dimensional network of 2k×k×k, and both the Y andZ dimension wraparounds are twisted by incrementing the X dimensioncoordinate by k. In the third case, a 2k×2k×k network, only the Zdimension wraparound is twisted, but values in both X and Y dimensionsare incremented during the twist.

In some implementations, the system 100 imposes constraints on the valueof k, which can allow for simpler and more efficient implementation ofthe switching interconnect fabric by reducing the need to support asmany configurations. For example, the system 100 may limit k to be amultiple of two, a multiple of four, etc. By limiting the values of k,the system limits the amounts or types of increments that the system 100needs to support in the interconnect fabric, as well as the amount ortype of twist that is permitted. For example, limiting k to multiples offour also limits the twist amounts to increments in multiples of four.

Routing of data within twisted torus networks can be performed similarto routing in traditional torus networks. Routes can be expressed as anumber of signed (e.g., direction-indicated) hops in the X, Y, and Zdimensions of the network with the sign selecting the direction (e.g.,+X vs. −X) A less obvious aspect of routing is how a givensource-destination pair is translated into a set of X, Y, Z hops so thatthe resulting route is minimal. The routing can be table-based, witheach node having a corresponding routing table for connections indifferent directions. The routes can be computed in advance and store(e.g., using Dykstra's algorithm) and then loaded by the system into therouting tables at initialization time. The selection and retrieval ofrouting information can be performed as part of initializing a nodenetwork for use by a user.

Another technique that can be used is virtual channels to avoiddeadlock. The system can populate the twisted-torus routing tables withdimension order routes, indicating which of the dimensions to travel inin which order. The system can follow a simple dateline rule to avoiddeadlocks: the packet virtual channel is incremented when traveling overa wraparound link and reset to zero when changing dimensions. Forexample, even though the “X” links may connect to a node whosecoordinates differ in X and in other dimensions (due to twisting), thisbasic dateline approach is sufficient to avoid deadlock.

One subtle routing issue is that for some source-destination pairs,there are multiple minimal routes. The canonical example occurs in atorus network occurs when routing exactly halfway around any of thetorus dimensions (e.g., 4 hops in a torus dimension of 8 nodes). One wayto achieve load balance in this case is to randomize the routes, e.g.,half the routes travel around the ring in one direction, half travel inthe other direction. In general, if there are multiple minimal routes,the system can choose among them with equal probability.

In some implementations, instead of randomizing routes (e.g., when routerandomization is not available), the system can vary the routing tablesfor each node in an attempt to improve load balance. In the torus, thereare simple strategies that are effective, such as to choose thedirection of routing in a ring for the halfway case by using the leastsignificant bit of the source node coordinate in that ring. Thisstrategy exactly load balances uniform random traffic.

It's less obvious how to derandomize the twisted tori torus routes in asimple way. This problem can be assessed as an integer linear programand the system can attempt to minimize the maximum channel load under auniform random traffic model. This computation reveals that it is notalways possible to achieve perfect load balance in twisted tori withdeterministic routing tables, but the system can get very close.

FIG. 6 is a table 600 showing different node and interconnectconfigurations and related characteristics.

The table 600 compares the performance of several practical-sized 3Dtorus and 3D twisted torus topologies. A uniform random traffic patternis used as a proxy to model the all-to-all patterns found in sparseembedding workloads. For this pattern, packets are sent between allsource-destination pairs with equal probability. Averaging over allpairs yields an average hop count and a maximum average channel load.For twisted tori, the table 600 shows the maximum average channel loadfor both randomized and deterministic routing.

FIG. 7 is a table 700 showing different node configurations and uniformrandom bandwidth measures of twisted torus interconnections compared tostandard torus interconnections. In a bandwidth-limited scenario, thetime to send a batch of uniform random packets is inversely proportionalto the maximum average channel load. In a 8×4×4 network, for example,this translates to a speedup of 1.0/0.578=−1.73 for the twisted torusover the non-twisted torus.

Twisted tori do not offer an asymptotic advantage over traditional tori.As the configuration is expanded to contain more chips, it oscillatesbetween cubical (e.g., 4×4×4) and non-cubical (e.g., 8×8×4)arrangements. The non-cubical configurations can be seen as intermediatesteps between two cubical configurations that differ by a factor of 8 inthe number of processing nodes. The twisted tori only outperform thetraditional tori for these intermediate configurations, but theadvantages can be quite significant for those intermediateconfigurations. Twisted tori also eliminate abrupt changes in networkperformance as a function of incremental changes in configuration size.

These performance measures show that twisted tori can improve theusability and efficiency of the network allocated from among the cluster111. Configuration size can be chosen to best fit the compute andcapacity requirements of the workload and the network performance scalesgracefully with that size. There are fewer “sharp corners” or steppedchanges in performance along the range of node sizes.

FIG. 8 is a table 800 showing various node network configurations andrelated properties.

A number of implementations have been described. Nevertheless, it willbe understood that various modifications may be made without departingfrom the spirit and scope of the disclosure. For example, various formsof the flows shown above may be used, with steps re-ordered, added, orremoved.

Embodiments of the invention and all of the functional operationsdescribed in this specification can be implemented in digital electroniccircuitry, or in computer software, firmware, or hardware, including thestructures disclosed in this specification and their structuralequivalents, or in combinations of one or more of them. Embodiments ofthe invention can be implemented as one or more computer programproducts, e.g., one or more modules of computer program instructionsencoded on a computer readable medium for execution by, or to controlthe operation of, data processing apparatus. The computer readablemedium can be a machine-readable storage device, a machine-readablestorage substrate, a memory device, a composition of matter effecting amachine-readable propagated signal, or a combination of one or more ofthem. The term “data processing apparatus” encompasses all apparatus,devices, and machines for processing data, including by way of example aprogrammable processor, a computer, or multiple processors or computers.The apparatus can include, in addition to hardware, code that creates anexecution environment for the computer program in question, e.g., codethat constitutes processor firmware, a protocol stack, a databasemanagement system, an operating system, or a combination of one or moreof them. A propagated signal is an artificially generated signal, e.g.,a machine-generated electrical, optical, or electromagnetic signal thatis generated to encode information for transmission to suitable receiverapparatus.

A computer program (also known as a program, software, softwareapplication, script, or code) can be written in any form of programminglanguage, including compiled or interpreted languages, and it can bedeployed in any form, including as a stand alone program or as a module,component, subroutine, or other unit suitable for use in a computingenvironment. A computer program does not necessarily correspond to afile in a file system. A program can be stored in a portion of a filethat holds other programs or data (e.g., one or more scripts stored in amarkup language document), in a single file dedicated to the program inquestion, or in multiple coordinated files (e.g., files that store oneor more modules, sub programs, or portions of code). A computer programcan be deployed to be executed on one computer or on multiple computersthat are located at one site or distributed across multiple sites andinterconnected by a communication network.

The processes and logic flows described in this specification can beperformed by one or more programmable processors executing one or morecomputer programs to perform functions by operating on input data andgenerating output. The processes and logic flows can also be performedby, and apparatus can also be implemented as, special purpose logiccircuitry, e.g., an FPGA (field programmable gate array) or an ASIC(application specific integrated circuit).

Processors suitable for the execution of a computer program include, byway of example, both general and special purpose microprocessors, andany one or more processors of any kind of digital computer. Generally, aprocessor will receive instructions and data from a read only memory ora random access memory or both. The essential elements of a computer area processor for performing instructions and one or more memory devicesfor storing instructions and data. Generally, a computer will alsoinclude, or be operatively coupled to receive data from or transfer datato, or both, one or more mass storage devices for storing data, e.g.,magnetic, magneto optical disks, or optical disks. However, a computerneed not have such devices. Moreover, a computer can be embedded inanother device, e.g., a tablet computer, a mobile telephone, a personaldigital assistant (PDA), a mobile audio player, a Global PositioningSystem (GPS) receiver, to name just a few. Computer readable mediasuitable for storing computer program instructions and data include allforms of non volatile memory, media and memory devices, including by wayof example semiconductor memory devices, e.g., EPROM, EEPROM, and flashmemory devices; magnetic disks, e.g., internal hard disks or removabledisks; magneto optical disks; and CD ROM and DVD-ROM disks. Theprocessor and the memory can be supplemented by, or incorporated in,special purpose logic circuitry.

To provide for interaction with a user, embodiments of the invention canbe implemented on a computer having a display device, e.g., a CRT(cathode ray tube) or LCD (liquid crystal display) monitor, fordisplaying information to the user and a keyboard and a pointing device,e.g., a mouse or a trackball, by which the user can provide input to thecomputer. Other kinds of devices can be used to provide for interactionwith a user as well; for example, feedback provided to the user can beany form of sensory feedback, e.g., visual feedback, auditory feedback,or tactile feedback; and input from the user can be received in anyform, including acoustic, speech, or tactile input.

Embodiments of the invention can be implemented in a computing systemthat includes a back end component, e.g., as a data server, or thatincludes a middleware component, e.g., an application server, or thatincludes a front end component, e.g., a client computer having agraphical user interface or a Web browser through which a user caninteract with an implementation of the invention, or any combination ofone or more such back end, middleware, or front end components. Thecomponents of the system can be interconnected by any form or medium ofdigital data communication, e.g., a communication network. Examples ofcommunication networks include a local area network (“LAN”) and a widearea network (“WAN”), e.g., the Internet.

The computing system can include clients and servers. A client andserver are generally remote from each other and typically interactthrough a communication network. The relationship of client and serverarises by virtue of computer programs running on the respectivecomputers and having a client-server relationship to each other.

While this specification contains many specifics, these should not beconstrued as limitations on the scope of the invention or of what may beclaimed, but rather as descriptions of features specific to particularembodiments of the invention. Certain features that are described inthis specification in the context of separate embodiments can also beimplemented in combination in a single embodiment. Conversely, variousfeatures that are described in the context of a single embodiment canalso be implemented in multiple embodiments separately or in anysuitable subcombination. Moreover, although features may be describedabove as acting in certain combinations and even initially claimed assuch, one or more features from a claimed combination can in some casesbe excised from the combination, and the claimed combination may bedirected to a subcombination or variation of a subcombination.

Similarly, while operations are depicted in the drawings in a particularorder, this should not be understood as requiring that such operationsbe performed in the particular order shown or in sequential order, orthat all illustrated operations be performed, to achieve desirableresults. In certain circumstances, multitasking and parallel processingmay be advantageous. Moreover, the separation of various systemcomponents in the embodiments described above should not be understoodas requiring such separation in all embodiments, and it should beunderstood that the described program components and systems cangenerally be integrated together in a single software product orpackaged into multiple software products.

In each instance where an HTML file is mentioned, other file types orformats may be substituted. For instance, an HTML file may be replacedby an XML, JSON, plain text, or other types of files. Moreover, where atable or hash table is mentioned, other data structures (such asspreadsheets, relational databases, or structured files) may be used.

Particular embodiments of the invention have been described. Otherembodiments are within the scope of the following claims. For example,the steps recited in the claims can be performed in a different orderand still achieve desirable results.

What is claimed is:
 1. A method performed by one or more computers, the method comprising: providing a cluster of processing nodes coupled using a reconfigurable interconnect fabric; determining (i) a number of processing nodes to allocate as a network within the cluster and (ii) a topology for the network, the topology having a length in each of multiple dimensions; selecting an interconnection scheme for the network, wherein the interconnection scheme is selected from a group that includes at least a torus interconnection scheme and a twisted torus interconnection scheme, wherein the selected interconnection scheme is a twisted torus interconnection scheme; allocating processing nodes for the network by allocating the determined number of processing nodes of the cluster in the topology; setting the reconfigurable interconnect fabric to provide the twisted torus interconnection scheme among the processing nodes allocated for the network, wherein the provided twisted torus interconnection scheme has an amount of twist that is selected based on the lengths of the topology, and wherein the provided twisted torus interconnection scheme applies an offset for the twist to one or more of the dimensions that are selected based on the lengths of the topology; and providing access to the network for performing a computing task.
 2. The method of claim 1, wherein selecting the interconnection scheme comprises selecting between the torus interconnection scheme and the twisted torus interconnection scheme based on the determined number of processing nodes.
 3. The method of claim 2, wherein the selected topology has a first size in a first dimension and a second size in a second dimension; and wherein selecting the interconnection scheme comprises selecting the twisted torus interconnection scheme based on determining that the first size is a multiple of the second size.
 4. The method of claim 1, wherein the topology for the network comprises an arrangement of nodes that extends along the multiple dimensions and includes multiple nodes along each of the multiple dimensions, wherein the topology has different amounts of nodes along at least two of the multiple dimensions; and wherein selecting the interconnection scheme comprises selecting the twisted torus interconnection scheme such that the network is symmetric.
 5. The method of claim 4, wherein the twisted torus interconnection scheme includes wraparound connections made using switching elements of the reconfigurable interconnect fabric; and wherein wraparound connections connect nodes or edges of the network that face opposite directions along a same dimension, wherein the wraparound connections for a first dimension in which the network is longest do not include any offsets in other dimensions, and wherein the wraparound connections for a second dimension in which the network is shorter than the first dimension has an offset in the first dimension.
 6. The method of claim 5, wherein the wraparound connections for the second dimension are each determined by connecting a starting node with an ending node that has: (i) a position in the second dimension that is the same as the starting node, and (ii) a position in the first dimension that is equal to a result of a modulo operation involving (a) a sum of a position of the starting node in the first dimension and a predetermined twist increment determined based on the topology and (b) a length of the longest dimension.
 7. The method of claim 1, wherein the topology is a two-dimensional topology.
 8. The method of claim 1, wherein the topology is a three-dimensional topology.
 9. The method of claim 1, wherein the cluster of processing nodes comprises multiple segments having a predetermined size and arrangement of multiple processing nodes, the segments having mesh connections between the nodes in each segment; and wherein the reconfigurable interconnect fabric comprises switching elements to permit dynamic, programmable reconfiguration of connections for external-facing data ports of processing nodes in each segment.
 10. The method of claim 9, wherein the segments are each a 4×4×4 group of processing nodes.
 11. The method of claim 1, wherein the processing nodes are each separate application specific integrated circuits (ASICs).
 12. The method of claim 1, wherein the reconfigurable interconnect fabric comprises switches for data-carrying optical signals.
 13. The method of claim 1, wherein the computing task comprises training a machine learning model.
 14. The method of claim 1, comprising: storing multiple configuration profiles specifying different configurations of the reconfigurable interconnect fabric to connect subsets of the processing nodes in the cluster; and selecting a configuration profile from among the multiple configuration profiles; wherein switching elements of the reconfigurable interconnect fabric are set according to the selected configuration profile.
 15. The method of claim 14, comprising initializing routing tables for processing nodes in the network based on stored routing information corresponding to the selected configuration profile.
 16. The method of claim 1, comprising allocating distinct networks of processing nodes in the cluster for different users, the distinct networks having different interconnection schemes.
 17. A system comprising: one or more computers; and one or more computer-readable media storing instructions that are operable, when executed by the one or more computers, to cause the one or more computers to perform operations comprising: providing a cluster of processing nodes coupled using a reconfigurable interconnect fabric; determining a number of processing nodes to allocate as a network within the cluster and iii) a topology for the network, the topology having a length in each of multiple dimensions; selecting an interconnection scheme for the network, wherein the interconnection scheme is selected from a group that includes at least a torus interconnection scheme and a twisted torus interconnection scheme, wherein the selected interconnection scheme is a twisted torus interconnection scheme; allocating processing nodes for the network by allocating the determined number of processing nodes of the cluster in the topology; setting the reconfigurable interconnect fabric to provide the twisted torus interconnection scheme among the processing nodes allocated for the network, wherein the provided twisted torus interconnection scheme has an amount of twist that is selected based on the lengths of the topology, and wherein the provided twisted torus interconnection scheme applies an offset for the twist to one or more of the dimensions that are selected based on the lengths of the topology; and providing access to the network for performing a computing task.
 18. One or more non-transitory computer-readable media storing instructions that are operable, when executed by one or more computers, to cause the one or more computers to perform operations comprising: providing a cluster of processing nodes coupled using a reconfigurable interconnect fabric; determining (i) a number of processing nodes to allocate as a network within the cluster and (ii) a topology for the network, the topology having a length in each of multiple dimensions; selecting an interconnection scheme for the network, wherein the interconnection scheme is selected from a group that includes at least a torus interconnection scheme and a twisted torus interconnection scheme, wherein the selected interconnection scheme is a twisted torus interconnection scheme; allocating processing nodes for the network by allocating the determined number of processing nodes of the cluster in the topology; setting the reconfigurable interconnect fabric to provide the twisted torus interconnection scheme among the processing nodes allocated for the network, wherein the provided twisted torus interconnection scheme has an amount of twist that is selected based on the lengths of the topology, and wherein the provided twisted torus interconnection scheme applies an offset for the twist to one or more of the dimensions that are selected based on the lengths of the topology; and providing access to the network for performing a computing task. 